Video: Writing Linear Equations in Standard Form

Write the linear equation 𝑦 = (3π‘₯ + 4)/12 in standard form.

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Video Transcript

Write the linear equation 𝑦 equals three π‘₯ plus four divided by 12 in standard form.

Standard form is 𝐴π‘₯ plus 𝐡𝑦 equals 𝐢, where 𝐴, 𝐡, and 𝐢 are constants. They’re the numbers. So essentially, we want to get π‘₯ and 𝑦 on one side of the equation and then a number all by itself on the other side of the equation.

Our first step would be to multiply both sides of the equation by 12. They cancel on the right-hand side. And we have that 12𝑦 is equal to three π‘₯ plus four. So we need to get π‘₯ on the left-hand side of the equation to be with the 𝑦. And then the four will be left by itself on the right.

So let’s go ahead and subtract three π‘₯ from both sides of the equation. The three π‘₯s cancel on the right. And then on the left, negative three π‘₯ and 12𝑦 cannot be put together. They’re different variables. And in standard form, the variable π‘₯ is written first and then the variable 𝑦. So we end up with negative three π‘₯ plus 12𝑦 equals four. So our linear equation written in standard form will be negative three π‘₯ plus 12𝑦 equals four.

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